FIG. 1 is a block diagram illustrating a known arrangement of a decision-feedback equalizer (DFE). In FIG. 1, an input terminal 5 is coupled to a source (not shown) of a sequence of signals each representing one of a constellation of ideal signal points in a planar signal space. Input terminal 5 is coupled to an input terminal of an FIR filter 10. An output terminal of the FIR filter 10 is coupled to an input terminal of a slicer 30 and to a first input terminal of a subtractor 40. An output terminal of the slicer 30 is coupled to a second input terminal of the subtractor 40 and to an output terminal 15. The output terminal 15 is coupled to a backend of a receiver (not shown) for decoding and utilizing the information encoded in the received signal. An output terminal of the subtractor 40 is coupled to an input terminal of a coefficient control circuit 20. An output terminal of the coefficient control circuit 20 is coupled to a control input terminal of the FIR filter 10.
In known equalizers such as illustrated in FIG. 1, the coefficient control circuit 20 implements a tap coefficient adaptation scheme, such as Least Mean Squares (LMS), to adjust the tap coefficients in the FIR filter 10. The subtractor 40 calculates an error signal E, which is the difference between the equalized received input signal from the FIR filter 10, representing a transmitted data symbol, and a sliced ideal signal from the slicer 30, representing the data symbol which is assumed to have been transmitted. In response to the error signal E, the coefficient control circuit 20 computes modified coefficient values for the FIR filter 10 taps to bring the equalized data signal closer to the ideal signal, hence achieving correct equalizer adaptation or convergence, all in a known manner.
Because in most cases the transmitted data is not known at the receiving end, the symbol assumed to have been transmitted must be estimated from the equalized data itself. A common way to provide such an estimation is called ‘slicing’, in which the decision of which symbol is assumed to have been transmitted is based on a plurality of pre-defined regions in the signal space, called ‘decision regions’. The decision region within which the received equalized signal lies determines the assumed transmitted symbol. Slicing works well when the large majority of the received equalized signals are in the correct decision regions and the slicing errors that do occur, happen in a random fashion such that they do not favor any of the regions neighboring the correct one. In this situation the average equalizer taps will converge.
A problem arises when signal impairments, such as residual carrier frequency and/or phase offset, cause slicing errors which favor one or more of the neighboring decision regions over others, i.e. the equalized data is consistently wrong in the long run. Such impairments potentially cause the equalizer taps to be driven towards incorrect steady-state values. In QAM modulation schemes this phenomenon can manifest itself in a form of a magnitude false-lock, where the tap magnitude of the equalizer taps is driven towards an incorrect steady-state average value.
FIG. 2 is a signal space diagram illustrating ideal and equalized received constellations useful in understanding the operation of the present invention. FIG. 2 illustrates a 16 QAM signal ideal constellation as filled in circles and equalized received signal points as hollow circles. Standard known decision regions are delimited by dotted lines. One skilled in the art will understand that these decision regions are rectangular regions disposed symmetrically around the ideal constellation points. Referring to FIG. 2a, the constellation of equalized received points (hollow circles) is smaller in magnitude than the constellation of ideal points, e.g. due to the presence of noise. In addition, the presence of a carrier phase and/or frequency offset causes the constellation of equalized received points to be rotated counterclockwise in the signal space.
More specifically, the equalized received point 5′ represents a transmitted symbol corresponding to that represented by the ideal point 5 in decision region d5. However, as described above, point 5′ is rotated counter-clockwise and is reduced in amplitude so that is lies in the decision region d1. Consequently, the slicer 30 when receiving a signal at point 5′ will make the incorrect decision that the symbol represented by ideal point 1 was transmitted. In addition, the difference between received point 5′ and ideal point 1 indicates that the magnitude of the received constellation is too large, and that the angle is correct. In response, the equalizer FIR filter 10 taps will be updated by the coefficient control circuit 20 to make the received constellation smaller.
It is conceivable, then, that if the right sequence of symbols occurs, the equalizer taps will be updated so that the equalized received constellation becomes so small that it becomes a ‘miniature’ version of the correct constellation that fits entirely inside the 4 innermost decision regions, as is illustrated in FIG. 2b. This is a stable false-lock situation, because this ‘mini’-constellation will always be sliced to the inner points 1-4 and hence its average power will be driven to correspond to a constant modulus ring passing through the inner points.
One known way to adapt the equalizer taps when correct slicer decisions cannot be made is called Constant Modulus Algorithm (CMA). The decisions made by the CMA algorithm do not coincide with ideal symbol signal locations. Instead, the CMA algorithm updates the tap coefficients in a manner which drives the average magnitude of the equalized received data toward the precalculated average magnitude of the ideal transmitted constellation, a magnitude value called the CMA ring radius. This method, however, is fairly crude and may converge towards a steady state with a residual rotational bias of the equalized constellation, thus resulting in overall decreased performance.
In some frequency-domain modulation schemes, such as the one used in Hiperlan2/IEE802.11a standards, the assumption of the frequency domain continuity between the adjacent equalizer taps is used to prevent a given equalizer tap value from being given a value which is too different from its neighbors. This method, however, is expensive to implement and its performance is highly dependent on the actual transmission channel frequency response.
A slicing algorithm which is simple and inexpensive to implement and which would, at the same time, combine the rotational invariance of the CMA with the unbiased steady-state constellation placement of the decision-directed methods is desirable.